Copper winding

Calculate the current flowing through the copper winding at an operating temperature of 70°C Celsius if the winding diameter is 1.128 mm and the coiled length is 40 m. The winding is connected to 8V.

Correct answer:

I =  9.5174 A

Step-by-step explanation:

$$\begin{gathered} U=8\text{V} \\ D=1.128\text{mm}\to \text{m}=1.128:1000\text{m}=0.00113\text{m} \\ l=40\text{m} \\ {t}_1=20\text{°C} \\ {t}_2=70\text{°C} \\ t=t_2-t_1=70-20=50\text{°C} \\ \alpha =0.004 \\ {\rho }_0=1.75\cdot 10^{-8}\doteq 1.75\cdot 10^{-8}\Omega \\ \rho ={\rho }_0\cdot (1+\alpha \cdot t)={\rho }_0\cdot (1+\alpha \cdot 50)\doteq 2.1\cdot 10^{-8}\Omega \\ r=D/2=0.0011/2\doteq 0.0006\text{m} \\ S=\pi \cdot r^2=3.1416\cdot 0.0006^2\doteq 9.9933\cdot 10^{-7}{\text{m}}^2 \\ R=\rho \cdot \frac{l}{S}=2.1\cdot 10^{-8}\cdot \frac{40}{9.9933\cdot 10^{-7}}\doteq 0.8406\Omega \\ I=\frac{U}{R}=\frac{8}{0.8406}=9.5174\text{A} \end{gathered}$$

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